The measurement of thermal conductivity is used frequently for analyzing gases, particularly for the quantitative analysis of two-component gas mixtures.
In principle, it holds true that the thermal conductivity of a gas or gas mixture varies with the mass of the gas molecules, their concentration and the temperature. If the (mixed-) thermal conductivity of the gas or the gas mixture is measured at a known gas temperature and for known components, then it is possible to exactly determine the concentrations of individual components of the gas mixture based on the thermal conductivity. Above all, the concentrations of hydrogen (H2) and helium (He) in the mixture with other gases such as air, oxygen (O2), nitrogen (N2), ammonia (NH3), argon (Ar), carbon dioxide (CO2), carbon monoxide (CO), chlorine (Cl2), hydrogen sulphide (H2S), methane (CH3), nitrogen monoxide (NO), dinitrogen monoxide (N2O) and water vapor (H2O) may be measured well, because these gases have particularly high thermal conductivity compared to the other gases. Thus, the thermal conductivity of hydrogen (H2) is λhydrogen=0.84 Wm−1K−1 and the thermal conductivity of helium (He) is λhelium=0.6 Wm−1K−1, while the thermal conductivity of air λair=0.012 Wm−1K−1 is less by approximately a factor 5-7.
To measure the thermal conductivity, a body is brought to a temperature TK which is higher than the ambient temperature TU. A gas (mixture) surrounding the body is generally at ambient temperature. For example, if the temperature difference ΔT=TK−TU is held constant, then the heating power PH necessary for this purpose is a measure for the thermal conductivity of the surrounding gas or gas mixture. Heating power PH is directly proportional to constantly retained temperature difference ΔT; the proportionality constant results from the product of the thermal conductivity λ and a (constant) geometry factor K which is a function of the measuring device. This correlation is described in equation (1):PH=KλΔT  (1)where PH designates the heating power, ΔT designates the temperature difference, K designates the geometry factor and λ designates the thermal conductivity.
Recently, micromechanical thermal-conductivity sensors based on silicon are increasingly being developed to determine thermal conductivity. In contrast to conventional thermal-conductivity sensors, these sensors have the feature of low power consumption, which essentially is no greater than the power consumption of the electronic equipment needed for the signal processing. Moreover, the miniaturized sensors possess short response times (time constants) which generally can only be achieved by the acceptance of a forced traversal with the measuring gas, i.e., a flow dependency, in the case of conventional sensors. In the last analysis, however, this makes universal use impossible. Finally, such micromechanical thermal-conductivity sensors based on silicon are economical to produce, because it is possible to fall back on customary methods for the production of integrated semiconductor components.
The design of a typical conventional micromechanical thermal-conductivity sensor based on silicon is shown in FIG. 1 and is described below.
A fundamental problem when measuring the thermal conductivity of a surrounding gas is the heat transfer caused by convection of the gas, accompanied by a falsification of the actual thermal-conductivity value. A convective heat transfer may result from external gas movements which become noticeable in the sensor, but also from the temperature difference, necessary for the measurement, between the heating element and diaphragm, respectively, and the gas.
It may be that a forced traversal of the thermal-conductivity sensor with the gas to be measured is definitely desired in order to permit a rapid gas exchange and therefore short response times; however, for micromechanical thermal-conductivity sensors having very small measuring volumes and an inherently rapid gas exchange thereby permitted, any convective heat transfer is regarded as disadvantageous.
To prevent convective heat transfer, the sensor is usually used in such a way that the gas volume near the diaphragm remains quiet. This may be achieved, for example, by covering the diaphragm with a cover plate.
For example, German Patent No. DE 37 252 describes a micromechanical thermal-conductivity sensor for measuring the thermal conductivity of a gas mixture, in which an insulator layer is applied on a support plate made of silicon, meander-shaped thin-film resistors being applied on the insulator layer by vapor deposition or sputtering. In the region of the thin-film resistors, the insulator layer is undercut so that in the support plate, a hollow is obtained which forms the lower part of the sensor measuring chamber. Resting on the support plate having the thin-film resistors is a silicon cover plate into which a hollow is etched at the height of the thin-film resistors which forms the upper part of the measuring chamber. The cover plate has an opening which, as a diffusion channel, makes it possible for the gas mixture to enter the measuring chamber. The exchange of gas in the lower hollow of the measuring chamber takes place through cutouts in the insulator layer.
The disadvantage in this thermal-conductivity sensor is that the dimensions of the diffusion channel must in any case be selected so that, first of all, the gas in the measuring chamber is exchanged as quickly as possible by diffusion through a large opening, but secondly, gas movements which occur outside of the measuring chamber are not transferred into the measuring chamber, which requires a small opening. However, this objective can only be achieved as a compromise between the two requirements, a given design of the diffusion channel generally no longer permitting a universal application.